Oxidation is loss of electron from the HOMO. The "ease of oxidation" is essentially captured in the ionization potential - that is, how much energy it takes to remove an electron from an orbital. While you can remove an electron from any molecular orbital, it is easiest to remove those with the highest energy - i.e., those from the HOMOs. The quantity of energy required to remove the electron is basically identical to how much the orbital (in this case the HOMO) is stabilized with respect to the "free electron limit". So the question you need to ask yourself is, of the triene or diene, which one has the more stabilized (lower energy) HOMO? The more stabilized orbital is lower energy, and there it takes more energy to remove an electron in it = harder to oxidize.